Launched in 2010, an investigation by Almunia has looked into whether Google gave undue preferential treatment to its own services in search results, to the detriment of other companies.

Almunia said that the US search engine giant must "offer remedies" to address the concerns, or face possible action, including a hefty fine.

Schmidt's letter has not been made public, but a Google spokesman said: "We have made a proposal to address the four areas the European Commission described as potential concerns. We continue to work co-operatively with the commission."

In May, the commissioner outlined four key areas where Google's practices "may be considered as abuses of dominance".

This includes the way in which Google displays "its own vertical search services differently" from competing products; the exclusivity Google sells for search terms; how Google copies content from other websites to its own services; and the restrictions placed on transferring advertising content to non-Google platforms.

A spokesman for Almunia confirmed receiving the letter, did but not give any further details.

It is thought that Almunia wants a swift settlement from Google, rather than a protracted legal battle with the firm.

But if Google fails to satisfy the commissioner, it could face a fine of up to 10% of its annual revenue. Based on last year's figures, that could be as much as $3.8bn (£2.4bn).